Exact Finite Difference Schemes

Many exact finite difference schemes for ODEs (ordinary differential equations) and PDEs (partial differential equations) are presented in this chapter. The exact finite difference schemes are usually presented in the form corresponding to the associated differential equations in order to provide the close link and relation between differential equations and difference equations and to help provide the insight into the construction of better finite difference schemes for more general differential equations. The majority of the examples provided in this chapter are NSFD (nonstandard finite difference) schemes and therefore, we demonstrate and highlight the values and insights of Mickens's NSFD schemes.